BSc Lond 1939, PhD 1944; DSc Manch 1962.
Barker was educated at Nottingham High School and University College, Nottingham. He was appointed assistant Lecturer in Chemistry at Nottingham in 1942. In 1946 he was appointed Lecturer in Chemistry at University of Manchester where he was promoted to Senior Lecturer in Biological Chemistry in 1959 and Reader in 1963. By 1970 he was professor. In 1962 Manchester awarded Barker a DSc in recognition of his research work in Chemistry and Biological Chemistry. He was particularly interested in nucleic acids in relation to growth and genetic characteristics in micro-organisms, plants and ascites tumour cells.